/* +++Date last modified: 05-Jul-1997 */

/*
**  CUBIC.C - Solve a cubic polynomial
**  public domain by Ross Cottrell
*/

#include <math.h>
#include <stdlib.h>
#include "snipmath.h"

void SolveCubic(double  a,
                double  b,
                double  c,
                double  d,
                int    *solutions,
                double *x)
{
      double    a1 = d_div(b,a), a2 = d_div(c,a), a3 = d_div(d,a);
      double    Q = d_div(d_add(d_mul(a1,a1),d_mul(-3.0,a2)),9.0);
      double    R = d_div(d_add(d_add(d_mul(2.0,d_pow(a1,3)),d_mul(d_mul(-9.0,a1),a2)),d_mul(27.0,a3)),54.0);
      double    R2_Q3 = d_add(d_mul(R,R),-(d_pow(Q,3)));

      double    theta;

      if (R2_Q3 <= 0)
      {
            *solutions = 3;
            theta = acos(R/d_sqrt(Q*Q*Q));
            x[0] = -2.0*d_sqrt(Q)*cos(theta/3.0) - a1/3.0;
            x[1] = -2.0*d_sqrt(Q)*cos((theta+2.0*PI)/3.0) - a1/3.0;
            x[2] = -2.0*d_sqrt(Q)*cos((theta+4.0*PI)/3.0) - a1/3.0;
      }
      else
      {
            *solutions = 1;
            x[0] = d_pow(d_add(d_sqrt(R2_Q3),fabs(R)), d_div(1,3.0));
            x[0] += Q/x[0];
            x[0] *= (R < 0.0) ? 1 : -1;
            x[0] -= a1/3.0;
      }
}

#ifdef TEST

int main(void)
{
      double  a1 = 1.0, b1 = -10.5, c1 = 32.0, d1 = -30.0;
      double  a2 = 1.0, b2 = -4.5, c2 = 17.0, d2 = -30.0;
      double  x[3];
      int     solutions;

      SolveCubic(a1, b1, c1, d1, &solutions, x);

      /* should get 3 solutions: 2, 6 & 2.5   */

      SolveCubic(a2, b2, c2, d2, &solutions, x);

      /* should get 1 solution: 2.5           */

      return 0;
}

#endif /* TEST */
